Lessons · Engineering · tolerance stacks
Tolerance stacks: when the parts all sit at their limits
Stack parts in a line and the nominals add, and so do the tolerances. Worst case is the plain sum; the statistical estimate is the root of the sum of squares.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Three spacers each within tolerance, and the assembly will not go into its housing. Nobody added the tolerances. The customer receives the one assembly where every part happened to be at its top limit on the same day.
How to think about it
Add the nominals for the nominal stack. Add the tolerances for the worst case; that is the number a fit must survive. If there are many parts and they are made independently, the root-sum-square is a fair estimate of what you will usually see, but it is not a guarantee.
Worked example
Worst case: nominals add, and tolerances addThe rule that guarantees the fit.
Three spacers: 5 ± 0.05, 12 ± 0.1, 8 ± 0.1 mmThe parts.
Nominal = 25 mm; worst-case ± 0.25 mm, so 24.75 to 25.25 mmEvery part at its limit in the same direction.
Statistical (RSS): sqrt(0.05² + 0.1² + 0.1²) = sqrt(0.0225) = ± 0.15 mmWhat you will usually see if the parts are many and independent. Not what you may promise.
Your turn
Parts 6 ± 0.1 and 9 ± 0.2. Write the worst-case tolerance.
± (0.1 + ) = ± 0.3 mm
Solve one, graded on the server
The trap
Averaging the tolerances, or assuming they cancel. Worst case is the sum: every part can sit at its limit on the same day, and the assembly that does not go together is the one that ships.